#### Vol. 301, No. 1, 2019

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Multiplicity upon restriction to the derived subgroup

### Jeffrey D. Adler and Dipendra Prasad

Vol. 301 (2019), No. 1, 1–14
##### Abstract

We present a conjecture on multiplicity of irreducible representations of a subgroup $H$ contained in the irreducible representations of a group $G$, with $G$ and $H$ having the same derived groups. We point out some consequences of the conjecture, and verification of some of the consequences. We give an explicit example of multiplicity $2$ upon restriction, as well as certain theorems in the context of classical groups where the multiplicity is $1$.

##### Keywords
reductive group, derived subgroup, representation, restriction, multiplicity
Primary: 22E50
##### Milestones
Received: 10 June 2018
Accepted: 5 September 2018
Published: 16 September 2019
##### Authors
 Jeffrey D. Adler Department of Mathematics and Statistics American University Washington, DC United States Dipendra Prasad Indian Institute of Technology Mumbai India Tata Institute of Fundamental Research Mumbai India Laboratory of Modern Algebra and Applications Saint-Petersburg State University Russia